1) What is the slope of the regression line (b_1)?
-.81; I shall not do the calculations here; many calculators have a statistical package.
2) What is the y-intercept (b_0) of the least squares regression line?
3.42; again, I shall not do the calculations.
3) What is the coefficient of determination (r^2) of x and y?
.98; (.976 rounds off to .98, the coefficient of determination is a square, hence is always non-negative.). If you calculated the y-hat values, you will need to carry 3 decimal places in the regression equation (rather than using the answers to 1 and 2 which are rounded off). This will not be the case on the actual final.
4) What is the standard deviation of the x values (s_x)?
2.217 (remember we are dividing by n-1, us the s or n-1 (not sigma or n) button if you are using your calculator)
5) Use the least squares regression line to estimate the value of y associated with x=2
1.7966; just plug 2 into the least squares regression line you found, 3.4 - .8(2) = 1.8
6) Greatest means consider only positive slopes, eyeballing the data reveals that any line near the data will have the greatest slope in c.
7) The coefficient of determination (but not the correlation) is always non negative, so we are looking for which data set lies closest to a line (relative to the vertical spread); the points in a are almost exactly on a line.
8) The spread in the horizontal direction is clearly least in a.
9) The slope and correlation have the same numerator (SSxy) and positive denominators. The coefficient of determination is never negative. The y-intercept can be positive, zero, or negative. The answer is a (the correlation)
10) What must be true if all the data lies in the first quadrant?
The mean of the x values (x-bar) is positive since it is obtained from adding positive numbers (and dividing by n). You can have lines with negative slope (hence negative correlation) which pass through points in the first quadrant. The answer is a.